"The objectivist view is that probabilities are real aspects of the universe - propensities of objects to behave in certain ways - rather than being just descriptions of an observer’s degree of belief. For example, the fact that a fair coin comes up heads with probability 0.5 is a propensity of the coin itself. In this view, frequentist measurements are attempts to observe these propensities. Most physicists agree that quantum phenomena are objectively probabilistic, but uncertainty at the macroscopic scale - e.g., in coin tossing - usually arises from ignorance of initial conditions and does not seem consistent with the propensity view." (Stuart J Russell & Peter Norvig, "Artificial Intelligence: A Modern Approach", 2010)
"It is the consistency of the information that matters for a good story, not its completeness. Indeed, you will often find that knowing little makes it easier to fit everything you know into a coherent pattern. (Daniel Kahneman, "Thinking, Fast and Slow", 2011)
"Knowing the importance of luck, you should be particularly suspicious when highly consistent patterns emerge from the comparison of successful and less successful firms. In the presence of randomness, regular patterns can only be mirages. (Daniel Kahneman, "Thinking, Fast and Slow", 2011)
"The reactions that break down large molecules into small ones do not require an input of energy, but the reactions that build up large molecules require and input of energy. This is consistent with the laws of thermodynamics, which say that large, orderly molecules tend to break down into small, disorderly molecules. (Stanley A Rice, "Life of Earth: Portrait of a Beautiful, Middle-aged Stressed-out World", 2011)
"While mathematicians now recognize that there is some freedom in the choice of the axioms one uses, not any set of statements can serve as a set of axioms. In particular, every set of axioms must be logically consistent, which is another way of saying that it should not be possible to prove a particular statement simultaneously true and false using the given set of axioms. Also, axioms should always be logically independent - that is, no axiom should be a logical consequence of the others. A statement that is a logical consequence of some of the axioms is a theorem, not an axiom. (John Tabak, "Beyond Geometry: A new mathematics of space and form", 2011)
"If the distance from the mean for one variable tends to be broadly consistent with distance from the mean for the other variable (e.g., people who are far from the mean for height in either direction tend also to be far from the mean in the same direction for weight), then we would expect a strong positive correlation. If distance from the mean for one variable tends to correspond to a similar distance from the mean for the second variable in the other direction (e.g., people who are far above the mean in terms of exercise tend to be far below the mean in terms of weight), then we would expect a strong negative correlation. If two variables do not tend to deviate from the mean in any meaningful pattern (e.g., shoe size and exercise) then we would expect little or no correlation." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"Complex systems defy intuitive solutions. Even a third-order, linear differential equation is unsolvable by inspection. Yet, important situations in management, economics, medicine, and social behavior usually lose reality if simplified to less than fifth-order nonlinear dynamic systems. Attempts to deal with nonlinear dynamic systems using ordinary processes of description and debate lead to internal inconsistencies. Underlying assumptions may have been left unclear and contradictory, and mental models are often logically incomplete. Resulting behavior is likely to be contrary to that implied by the assumptions being made about' underlying system structure and governing policies. (Jay W Forrester, "Modeling for What Purpose?", The Systems Thinker Vol. 24 (2), 2013)
"A worldview is a commitment, a fundamental orientation of the heart, that can be expressed as a story or in a set of presuppositions (assumptions which may be true, partially true or entirely false) which we hold (consciously or subconsciously, consistently or inconsistently) about the basic constitution of reality, and that provides the foundations on which we live and more and have our being." (James W Sire,"Naming the Elephant: Worldview as a Concept", 2015)
"Accuracy and coherence are related concepts pertaining to data quality. Accuracy refers to the comprehensiveness or extent of missing data, performance of error edits, and other quality assurance strategies. Coherence is the degree to which data - item value and meaning are consistent over time and are comparable to similar variables from other routinely used data sources." (Aileen Rothbard, "Quality Issues in the Use of Administrative Data Records", 2015)
"Reality is necessarily viewed through a conceptual system and is inseparable from the system through which it is viewed. But reality is by definition singular - there is only one reality; there cannot be two or three. Something is either real or it is not. The notion that reality is relative or that there can be two competing and inconsistent realities is disorienting and produces untenable cognitive dissonance." (William Byers, "Deep Thinking: What Mathematics Can Teach Us About the Mind", 2015)
"The essential quality of mathematics that binds it together in a coherent way is the use of mathematical proof to deduce new results from known ones, building up a strong and consistent theory." (Ian Stewart & David Tall, "The Foundations of Mathematics" 2nd Ed., 2015)
"Like all models, people’s mental models are an abstraction of reality. They may be complete and correct, or they may have gaps or inconsistencies that are consequential to effective decision making and action. A mental model is usually less complex than the real-world phenomenon involved and tends to lag in context or time and so can easily become out of date. In many cases, people may lack conscious, well-formed mental models on issues that they have not thoroughly considered in the past. This may be challenging for decision-makers as people’s responses may seem unpredictable or irrational. (Matthew D Wood, An Introduction to Mental Modeling, [in "Mental Modeling Approach: Risk Management Application Case Studies"], 2017)
"Quaternions are not actual extensions of imaginary numbers, and they are not taking complex numbers into a multi-dimensional space on their own. Quaternion units are instances of some number-like object type, identified collectively, but they are not numbers (be it real or imaginary). In other words, they form a closed, internally consistent set of object instances; they can of course be plotted visually on a multi-dimensional space but this only is a visualization within their own definition." (Huseyin Ozel, "Redefining Imaginary and Complex Numbers, Defining Imaginary and Complex Objects", 2018)
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